Sponsor:
This research was partially supported by
Spanish Ministry of Education and Science grant 2007/04438/001, by Madrid Region
grant 2011/00068/001, by Spanish Ministry of Science and Innovation grant
2012/00084/001 and by MCI grant MTM2008-03010.

Abstract:

Functional data are becoming increasingly available and tractable because of the last
technological advances. We enlarge the number of functional depths by defining two
new depth functions for curves. Both depths are based on a spatial approach: the
functional spatial depth (FSD), that shows an interesting connection with the functional
extension of the notion of spatial quantiles, and the kernelized functional spatial depth
(KFSD), which is useful for studying functional samples that require an analysis at a
local level. Afterwards, we consider supervised functional classification problems, and
in particular we focus on cases in which the samples may contain outlying curves. For
these situations, some robust methods based on the use of functional depths are
available. By means of a simulation study, we show how FSD and KFSD perform as
depth functions for these depth-based methods. The results indicate that a spatial depthbased
classification approach may result helpful when the datasets are contaminated,
and that in general it is stable and satisfactory if compared with a benchmark procedure
such as the functional k-nearest neighbor classifier. Finally, we also illustrate our
approach with a real dataset.